Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
Target Test Prep GRE Quant is a unique, comprehensive online course that combines innovative software with time-tested study methods to prepare you for the rigors of the GRE. Try our course for 5 days for just $1(no automatic billing)
Regardless of whether you choose to study with Greenlight Test Prep, we believe you'll benefit from these free resources. Free GRE Prep Study Guide, Free Video Modules, and more
Four women and three men must be seated in a row for a group
[#permalink]
06 Jun 2017, 13:05
2
Expert Reply
8
Bookmarks
00:00
Question Stats:
55% (01:57) correct
44% (02:38) wrong based on 65 sessions
HideShow
timer Statistics
Four women and three men must be seated in a row for a group photograph. If no two men can sit next to each other, in how many different ways can the seven people be seated?
Four women and three men must be seated in a row for a group
[#permalink]
07 Jun 2017, 15:02
3
Expert Reply
1
Bookmarks
GreenlightTestPrep wrote:
Four women and three men must be seated in a row for a group photograph. If no two men can sit next to each other, in how many different ways can the seven people be seated?
A) 240 B) 480 C) 720 D) 1440 E) 5640
Take the task of arranging the 7 peopl and break it into stages.
Stage 1: Arrange the 4 women in a row We can arrange n unique objects in n! ways. So, we can arrange the 4 women in 4! ways (= 24 ways) So, we can complete stage 1 in 24 ways
IMPORTANT: For each arrangement of 4 women, there are 5 spaces where the 3 men can be placed. If we let W represent each woman, we can add the spaces as follows: _W_W_W_W_ So, if we place the men in 3 of the available spaces, we can ENSURE that two men are never seated together.
Let's let A, B and C represent the 3 men.
Stage 2: Place man A in an available space. There are 5 spaces, so we can complete stage 2 in 5 ways.
Stage 3: Place man B in an available space. There are 4 spaces remaining, so we can complete stage 3 in 4 ways.
Stage 4: Place man C in an available space. There are 3 spaces remaining, so we can complete stage 4 in 3 ways.
By the Fundamental Counting Principle (FCP), we can complete the 4 stages (and thus seat all 7 people) in (24)(5)(4)(3) ways (= 1440 ways)
Re: Four women and three men must be seated in a row for a group
[#permalink]
22 Aug 2018, 00:49
May I know why is it when we place the men, we don't follow the reasoning where since there are three men, there are three men to choose from, hence 3x, followed by 2x and 1x. Instead, we follow the reasoning of the available chairs instead i.e. 5 chairs, then 4, then 3. I agree with your way as it seems correct but I can't grasp the logic behind it. Thanks for helping me to better understand.
Re: Four women and three men must be seated in a row for a group
[#permalink]
22 Aug 2018, 16:12
Expert Reply
Runnyboy44 wrote:
May I know why is it when we place the men, we don't follow the reasoning where since there are three men, there are three men to choose from, hence 3x, followed by 2x and 1x. Instead, we follow the reasoning of the available chairs instead i.e. 5 chairs, then 4, then 3. I agree with your way as it seems correct but I can't grasp the logic behind it. Thanks for helping me to better understand.
Say there are 9 chairs so then there is a blank space to the left of a woman and a blank space to the right. Like below
_ _ _ _ _ _ _ _ _
So we can place women on chair 2 chair 4....chair 8.
Chair 2: 4 woman available for seating
Chair 4: 3 woman available for seating
Chair 6: 2 woman available for seating
Chair 8: 1 woman available for seating
So total ways = \(4 \times 3 \times 2 \times 1= 4!=24\).
Now blanks spaces available for man_1 = 5; man_2= 4; man_3=3
Total ways is \(5 \times 4 \times 3= 60\).
In the first case we are arranging the women in the second case we are arranging the blanks. When we say no two man can sit together the positions of women are fixed: i.e. 2, 4, 6, 8. Position of men are not fixed. So a viable arrangement can be:
M-W-W-M-W-M-W vs W-W-M-W-M-W-M.
If you had only 3 places for men to sit then the only viable combination would have been \(3 \times 2 \times 1= 3!\) just like the women case but here we have 5 places and 3 men, hence \(5 \times 4 \times 3=60\).
Note this is also called arranging m things in n places and it is represented by:
Re: Four women and three men must be seated in a row for a group
[#permalink]
30 Oct 2018, 11:55
Why do we have to find the ways to arrange the women first? Would it be possible to solve this problem by finding all the different ways of arranging the 7 people then subtract out the number of arrangements that violate the restriction?
Re: Four women and three men must be seated in a row for a group
[#permalink]
30 Oct 2018, 12:11
Expert Reply
msawicka wrote:
Why do we have to find the ways to arrange the women first? Would it be possible to solve this problem by finding all the different ways of arranging the 7 people then subtract out the number of arrangements that violate the restriction?
There's only one way to find out . . .
_________________
Re: Four women and three men must be seated in a row for a group
[#permalink]
03 Jun 2021, 13:03
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.